Thomas Young WAITSFIELD ELEMENTARY SCHOOL, WAITSFIELD, VT
1st Grade Math : Unit #11 - The Number 10 and the Addition and Subtraction Concept : Lesson #17

Assessment of Unit Concepts: Addition and Subtraction Story Problems

Objective: SWBAT solve addition and subtraction story problems. SWBAT identify a strategy used to solve the problem and accurately record their answers.
Standards: 1.OA.A.1 1.OA.C.6 1.NBT.C.5 MP1 MP2 MP3 MP4
Subject(s): Math
60 minutes
1 Warm Up - 10 minutes

Please note that I completed this assessment over a couple of days. Unless you have a very small class, you'll probably have to plan on doing it over a couple of days, too.

Advanced Preparation:  In order to use this activity, you will need to make sets of drop sticks. Each set consists of 10 tongue depressors/craft sticks.  On one side of each stick, you will need to draw 10 dots.  On the other side of the stick, you will need to draw one dot.  

"I want to talk about the ten stick game that you have played before.  I noticed that many of you drop the sticks and then sort them by 10's and 1's and then count them.  This is a strategy that works but I want to offer you a challenge to the game.  Once you drop them, I just want you to "untangle" them.  What I mean is to straighten them out but don't organize them by 10's and 1's. Once you have untangled them, I want you to try and count them in the order they are laying.  I will now model this for you (see Demonstrating Drop Sticks With Change in section resource)."

I will model this one or two times and then ask a student or two to model it for the class too.

"I would now like a volunteer to model this new way of playing."

"Now you will play on your own. If you want to try this challenging way, you can do so, or you can revert back to another strategy for finding the total number of dots."

As students are playing, I will circulate about the group, observing how students are playing the game and/or which strategy they are using to find the total amount of dots.

I am introducing the change in this activity as a reassessment for my next unit. The next unit will focus on the skills of counting on and off the decade by 10's and 10 more or 10 less than a number. This activity will give me a quick idea of where students are with their ability to count on and off the decade.  

In this activity, the students are demonstrating that they understand (or are developing an understanding) that two digit numbers are made up of a group of 10's and some 1's, that numbers 1, 2, 3, 4, … 9 in each two digit number, starting with one of those numbers, represents a group of tens, and that they can start at any number and add to more to that number (CCSS.MATH.CONTENT.1.NBT.B.2,CCSS.MATH.CONTENT.1.NBT.C.5).

An A-Ha Moment
Developing a Conceptual Understanding

As students were engaged with this activity, one student pointed out that they could figure out how many dots there were just by counting the tens or the ones.  He realized that there were ten sticks and connected that to groups of tens and ones to make 100.  I had him present his thinking to the rest of the class before we moved on to the next part of the lesson.

His presentation is the video in the resources of this reflection.

2 Students Modeling Work - 15 minutes

I have the students face the smart board and will use this time for a few of them to present the strategies that they used to solve story problems in the previous lesson. I have identified beforehand which students I want to present.  I am being strategical in the work that is being modeled because I want students to see specific strategies that were used.  We have been working on these strategies over the past few weeks and at this point I am expecting all students to be counting on or counting back (at minimum) when solving story problems.  If a students is still counting all or drawing all and then subtracting or adding, they are not meeting the expectation at this point of in the year.  

"Yesterday, you all worked on several story problems that involved addition and subtraction.  Now, I am going to ask a few of you to present how you solved a specific problem."

I then share three examples of student work.  I will start with a student who used a number line but had an organizational error (see section resource).  After she presents, I will ask if anyone sees or point out that her strategy was appropriate and efficient but that she made an organizational error with her hops and numbers.  In this case students have the opportunity to distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is (CCSS.MATH.PRACTICE.MP3).

The second example (also in the section resource) is of a student who used his knowledge of one fact to quickly figure out the answer to another fact.  

I will end with one last student correctly modeling the appropriate use of using a number line and recording with an correct equation.  I didn't include a video of this but you can get the gist from the other two videos.

3 Assessment: Addition and Subtraction Story Problems - 45 minutes

Advanced Preparation:  You will need to make enough cope soy the assessment problems for each student.

"You are now going to work on solving your own problems. I will read the first problem to each of you and then have you go work on your own.  If you need help reading any problem, just let me know.  Remember, I want you to use a strategy that we have talked about and I want you to record your thinking."

It is important that you circulate and observe how students are solving these problems.  1st grade students can't always represent their thinking completely.  It is with this in mind that you want to check in with students, especially those who you know may struggle with this more than others.

In this situation, students are solving story problems (with in 20) that require them to add to and take away from using a organized strategy (CCSS.MATH.CONTENT.1.OA.A.1).

By asking students to solve story problems, the students are demonstrating the ability to explain the meaning of a problem and look for entry points to its solution (CCSS.MATH.PRACTICE.MP1).

The last question on this page asks students to explain how solving 6+4 helps you solve 16+4.  It is the flexibility in their thinking and understanding of making groups of 10, that allows them to connect the relationship of these two number sets (CCSS.MATH.PRACTICE.MP2)

Looking At Student Work: Meeting the Standard
Unit Exams

When looking at the students work, you want to make sure that students can make sense of the action in the story by choosing the correct operation and create an accurate equation. You'll also want to note:

  • what strategies do they use?
  • do they get the right answer?
  • do they see the relationship between the numbers in the last two questions of the assessment?

The examples included show how this student used a number line to solve each task.  She also demonstrates that she understands the relationship between making 10 and making 20.  

It is important that students represent counting back from right to left to signify that they are moving down the number line when they are solving removal situations.

4 1:1 Assessment on Addition and Subtraction Facts - 40 minutes

This assessment will be done 1:1 with each child.  It will give you a quick sampling of strategies that students are using to solve addition and subtraction facts.  You will have the students fill out the student recording sheet and you will fill out the teacher sheet at the same time. Completed examples of these sheets are in the section's resources. These sheets are part of the assessment packet that you printed out in the last section.  

As students finish their story problems, they start working on the station time activities.  This way you can pull kids to do this 1:1 assessment piece.  I time the students, so that I can get an idea how quickly they can do a set of facts.  The assessment also allows me to see if they can switch from addition to subtraction and back to addition problems (are they noticing the signs).  

"I am going to ask you to solve some equations.  If you know the fact, I just want you to write it.  If you need to use a strategy, I would like you to do it out loud so that I can tell who you are solving the equations."

It is the expectation that students can add and subtract within 10 fluently (CCSS.MATH.CONTENT.1.OA.C.6).

5 Station Time Activities - 45 minutes

As students finish the story problem tasks, they will work on one of the station actives listed below. These are all activities that have been played in previous lessons.

  • Recording Differences:  There is a detailed description of this activity in the linked lesson.  There is also a video in this section resources.  The recording sheet for this activity is also in the section resource.  This activity allows students to develop fluency with subtraction facts within 12.
  • Twenty/Twenty:  There is a detailed description of this activity in the linked lesson.  This activity allows students to add at least three addends to create 20.  It also allows the opportunity for students to use their understanding of 10 to solve for 20.  
  • Finding the Difference:  There is a video in the section resource that has two students explaining how to play this game.  The recording sheet for this game is also in the section resource.  This activity is meant for students who are fluent with their with in 10 subtraction facts and will now move onto subtracting from teen numbers.
6 Lesson Wrap Up - 15 minutes

I finish this lesson by gathering the students back to the carpet to solve a two more story problems as a group.  I want to close the lesson by reiterating the desired strategies for solving story problems where there is a removal situation.  

"I want to read another problem to you.  I had thirteen balloons.  Four of them popped. How many balloons do I have left?  Who can describe a way that they would solve this question."

I then take suggestion and illustrate their ideas on the board.  Each time, I am asking, "who else would have solved it that way?"

The photo in the section's resources shows the different ways that students suggested to solve the problem.

I then end with one last question and model using the number line to count back.  I want to end with students hearing this last.  This way they finish thinking about this strategy.  The example of this is on the bottom of the photo in the section's resources.

This discussion allows students to represent their thinking in a mathematical way (CCSS.MATH.PRACTICE.MP4).

7 Continued Practice - 5 minutes

I will ask the students to meet me on the carpet and hand out their sheet for today's Mad Minute exercise.  This routine was introduced in a previous lesson.  Please check out the link to get a full overview of this routine.

I want to really focus on fact fluency and build upon the students ability to solve within ten fluently (CCSS.MATH.CONTENT.1.OA.C.6).  I am going to use the Mad Minute Routine.  This is a very "old school" routine.  However, I truly feel students need practice in performing task for fluency in a timed fashion.  Students need to obtain fact fluency in order to have success with multiplicative reasoning.  Students who don't gain this addition fact fluency by the end of 2nd grade tend to struggle with the multiplicative reasoning in third.  Having this fluency also allows them to work on more complex tasks because the have the fact recall to focus on the higher level concepts.